First slide
Resistivity of various materials

Two metal wires of identical dimensions are connected in series. If σ1 and σ2  are the conductivities of the metal wires respectively, the effective conductivity of the combination is


As both metal wires are of identical dimensions, so their length and area of cross-section will be same. Let them be I and A respectively. Then The resistance of the first wire is

R1=lσ1A                                ....(i)

and that of the second wire is 

R2=lσ2A                       ...(ii)

As they are connected in series, so their effective resistance is


=lσ1A+lσ2A  ( using (i) and  (ii))

=lA1σ1+1σ2                  . . .(iii)

If σeff is the effective conductivity of the combination, then

Rs=2lσeff A                        . . . .(iv)

Equating eqns. (iii) and (iv), we get 


2σeff =σ2+σ1σ1σ2σeff =2σ1σ2σ1+σ2


Get Instant Solutions
When in doubt download our app. Now available Google Play Store- Doubts App
Download Now
Doubts App